But in general, the idea is that in order for something to boil, enough energy must be absorbed by it to cause vibrations large enough to enhance the kinetic energy of each molecule to the point where they break away from the coulombic forces that hold them together in the original liquid.

When a more massive solid is dissolved into such a liquid, the energy goes into not only exciting each water molecule to a higher kinetic energy but also each salt molecule to a higher kinetic energy. The more massive salt molecules themselves need a larger contribution of energy in order to excite them. This takes away from the contribution to the water molecules. The increased density ends up requiring more energy for the same amount of excitation that would lead to the boiling of the water.

Put another way, the salt molecules weigh down the water molecules and restrict their movement. This perhaps is easier to visualize.